| Day | Topics | Reading |
|---|---|---|
| Mo. 8/21 | The Integers. | [OS] Sec. 1.1 |
| We. 8/23 | Groups: Basic Properties | [OS] Sec. 1.1, 2.1 |
| Fr. 8/25 | The Euclidean algorithm; Structure in Z/n. | [OS] Sec 1.1-, 2.1 |
| Mo. 8/28 | Groups, Subgroups, Order, Lattice Diagrams | [OS] Sec 1.2, 2.1-2 |
| We. 8/30 | Homomorphisms, isomorphisms. Direct product. | [OS] Sec 2.2, 2.3. |
| Fr. 9/1 | Lattice Diagrams (group work). | [OS] Sec 2.2, 2.3. |
| We. 9/6 | Direct products, group generated by a subset kernel, image of a homomorphism |
[OS] Sec. 2.2,3 (and some extra material) |
| Fr. 9/8 | (group work)Permutation groups. | [OS] Sec. 2.4 |
| Mo. 9/11 | . Permutation groups, the alternating group An
Cayley's theorem. |
[OS] Sec. 2.4 |
| We. 9/13 | Cosets and Conjugates. | [OS] Sec. 2.5, 2.6 |
| Fr. 9/13 | Symmetric group (group work). | [OS] Sec. 2.4-6 |
| Mo. 9/11 | Normal subgroups and isomorphism theorems . | [OS] Sec. 2.7 |
| We. 9/13 | Matrix groups. | [OS] Sec. 2.8 |
| Fr. 9/15 | Cayley's theorem and S_n generators (group work). | [OS] Sec 2.4, 2.6-7 |
| Mo. 9/18 | Some problems from Problem Set 3. Quotient groups. |
[OS] Sec. 2.6-7 |
| We. 9/20 | Quotient groups What does isomorphismic mean? isomorphism/factor theorems . |
[OS] Sec. 2.7,9 |
| Fr. 9/22 | Lattices and quotient groups (group work). | [OS] Sec. 2.7-9 |
| Mo. 9/25 | Factor, Correspondence and 3rd isomorphism theorems, lattices of subgroups. |
[OS] Sec. 2.7,9 |
| We. 9/27 | Matrix groups. | [OS] Sec. 2.10 |
| Fr. 9/29 | TEST #1. | [OS] Ch. 2 |
| Mo. 10/2 | The second isomorphism theorem. | [OS] Sec. 3.1 |
| We. 10/4 | Semi-direct products. | [OS] Sec.3.1 |
| Fr. 10/6 | External semi-direct products (group work). | [OS] Sec. 3.1 |
| Mo. 10/9 | Matrix Groups (group work). | [OS] Sec. 2.8, 3.1 |
| We. 10/11 | Counting the general linear group. | [OS] Sec. 2.8 |
| Fr. 10/13 | Finite Abelian Groups. | [OS] Sec. 3.2 |
| Mo. 10/16 | Simple groups and An. | [OS] Sec. 3.3 |
| We. 10/18 | Semi-direct products and Aut(Z_n). | [OS] Sec. 3.2 |
| Fr. 10/20 | Rings, units zero-divisors, nilpotents. | [OS] Sec. 4.1,2 |
| Mo. 10/23 | Ring homomorphisms and constructions. | [OS] Sec. 4.1,2 |
| We. 10/25 | Finitely generated abelian groups (group work). | [OS] Sec. 3.3 |
| Fr. 10/27 | TEST #2 Group theory 1:00-3:00 GMCS room 307 | [OS] Sec. Ch 2, 3 |
| Mo. 10/30 | (group work) HW 8. | [OS] Sec. 4.1,2,3 |
| We. 11/1 | Ideals. | [OS] Sec. 4.1,2,3,4 |
| Fr. 11/3 | Ideals, quotient rings and the isomorphism theorems . | [OS] Sec. 4.4,5 |
| Mo. 11/6 | Ideals and quotient rings (group work) HW 9. | [OS] Sec. 4.4,5,6 |
| We. 11/8 | Maximal, prime and radical ideals, HW 9. | [OS] Sec. 4.6 |
| Mo. 11/13 | Isomorphism theorems. Roots, factors theorem | [OS] Sec. 4.5 |
| We. 11/15 | Rings of fractions in Q (group work) HW 11. | [OS] Sec. 4.7 |
| Fr. 11/17 | Constructing rings of fractions. | [OS] Sec. 4.7 |
| Mo. 11/20 | Complex numbers; Fundamental theorem of algebra. Gaussian numbers. | [OS] Sec. 1.2 |
| Mo. 11/27 | Fields. | [OS] Sec. 5.1-2 |
| We. 11/29 | Finite fields (group work) HW 11. | [OS] Sec. 5.3 |
| Fr. 12/1 | Finite fields main theorem . | [OS] Sec. 5.3 |
| Mo. 12/4 | Finite Fields and Number fields. | [OS] Sec. 5.4 |
| We. 12/6 | Cyclotomic number fields (group work). | [OS] Sec. |
| Fr. 12/8 | Number Fields Problems (group work). | [OS] Sec. |
| Mo. 12/11 | Formation of fractions and other review. | [OS] Sec. |
| We. 12/13 (8:00-10:00) | FINAL . | [OS] Sec. |